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Unitary Representations And Harmonic Analysis
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Book Synopsis Unitary Representations and Harmonic Analysis by : M. Sugiura
Download or read book Unitary Representations and Harmonic Analysis written by M. Sugiura and published by Elsevier. This book was released on 1990-03-01 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: The principal aim of this book is to give an introduction to harmonic analysis and the theory of unitary representations of Lie groups. The second edition has been brought up to date with a number of textual changes in each of the five chapters, a new appendix on Fatou's theorem has been added in connection with the limits of discrete series, and the bibliography has been tripled in length.
Book Synopsis Representation Theory and Complex Analysis by : Michael Cowling
Download or read book Representation Theory and Complex Analysis written by Michael Cowling and published by Springer. This book was released on 2008-02-22 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Six leading experts lecture on a wide spectrum of recent results on the subject of the title. They present a survey of various interactions between representation theory and harmonic analysis on semisimple groups and symmetric spaces, and recall the concept of amenability. They further illustrate how representation theory is related to quantum computing; and much more. Taken together, this volume provides both a solid reference and deep insights on current research activity.
Book Synopsis Harmonic Analysis on Commutative Spaces by : Joseph Albert Wolf
Download or read book Harmonic Analysis on Commutative Spaces written by Joseph Albert Wolf and published by American Mathematical Soc.. This book was released on 2007 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study starts with the basic theory of topological groups, harmonic analysis, and unitary representations. It then concentrates on geometric structure, harmonic analysis, and unitary representation theory in commutative spaces.
Book Synopsis Harmonic and Applied Analysis by : Stephan Dahlke
Download or read book Harmonic and Applied Analysis written by Stephan Dahlke and published by Birkhäuser. This book was released on 2015-09-12 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume explores the connection between the theoretical aspects of harmonic analysis and the construction of advanced multiscale representations that have emerged in signal and image processing. It highlights some of the most promising mathematical developments in harmonic analysis in the last decade brought about by the interplay among different areas of abstract and applied mathematics. This intertwining of ideas is considered starting from the theory of unitary group representations and leading to the construction of very efficient schemes for the analysis of multidimensional data. After an introductory chapter surveying the scientific significance of classical and more advanced multiscale methods, chapters cover such topics as An overview of Lie theory focused on common applications in signal analysis, including the wavelet representation of the affine group, the Schrödinger representation of the Heisenberg group, and the metaplectic representation of the symplectic group An introduction to coorbit theory and how it can be combined with the shearlet transform to establish shearlet coorbit spaces Microlocal properties of the shearlet transform and its ability to provide a precise geometric characterization of edges and interface boundaries in images and other multidimensional data Mathematical techniques to construct optimal data representations for a number of signal types, with a focus on the optimal approximation of functions governed by anisotropic singularities. A unified notation is used across all of the chapters to ensure consistency of the mathematical material presented. Harmonic and Applied Analysis: From Groups to Signals is aimed at graduate students and researchers in the areas of harmonic analysis and applied mathematics, as well as at other applied scientists interested in representations of multidimensional data. It can also be used as a textbook for graduate courses in applied harmonic analysis.
Book Synopsis Unitary Representations of Reductive Lie Groups by : David A. Vogan
Download or read book Unitary Representations of Reductive Lie Groups written by David A. Vogan and published by Princeton University Press. This book was released on 1987-10-21 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an expanded version of the Hermann Weyl Lectures given at the Institute for Advanced Study in January 1986. It outlines some of what is now known about irreducible unitary representations of real reductive groups, providing fairly complete definitions and references, and sketches (at least) of most proofs. The first half of the book is devoted to the three more or less understood constructions of such representations: parabolic induction, complementary series, and cohomological parabolic induction. This culminates in the description of all irreducible unitary representation of the general linear groups. For other groups, one expects to need a new construction, giving "unipotent representations." The latter half of the book explains the evidence for that expectation and suggests a partial definition of unipotent representations.
Book Synopsis Abstract Harmonic Analysis of Continuous Wavelet Transforms by : Hartmut Führ
Download or read book Abstract Harmonic Analysis of Continuous Wavelet Transforms written by Hartmut Führ and published by Springer. This book was released on 2005-01-17 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a systematic discussion of wavelet-type inversion formulae based on group representations, and their close connection to the Plancherel formula for locally compact groups. The connection is demonstrated by the discussion of a toy example, and then employed for two purposes: Mathematically, it serves as a powerful tool, yielding existence results and criteria for inversion formulae which generalize many of the known results. Moreover, the connection provides the starting point for a – reasonably self-contained – exposition of Plancherel theory. Therefore, the volume can also be read as a problem-driven introduction to the Plancherel formula.
Book Synopsis A Course in Abstract Harmonic Analysis by : Gerald B. Folland
Download or read book A Course in Abstract Harmonic Analysis written by Gerald B. Folland and published by CRC Press. This book was released on 2016-02-03 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Course in Abstract Harmonic Analysis is an introduction to that part of analysis on locally compact groups that can be done with minimal assumptions on the nature of the group. As a generalization of classical Fourier analysis, this abstract theory creates a foundation for a great deal of modern analysis, and it contains a number of elegant resul
Book Synopsis Harmonic Analysis on Free Groups by : Figa-Talamanca
Download or read book Harmonic Analysis on Free Groups written by Figa-Talamanca and published by CRC Press. This book was released on 1983-08-17 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an account of recent results on the theory of representations and the harmonic analysis of free groups. It emphasizes the analogy with the theory of representations of noncompact semisimple Lie groups and restricts the focus to a class of irreducible unitary representations.
Book Synopsis Non-Abelian Harmonic Analysis by : Roger E. Howe
Download or read book Non-Abelian Harmonic Analysis written by Roger E. Howe and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book mainly discusses the representation theory of the special linear group 8L(2, 1R), and some applications of this theory. In fact the emphasis is on the applications; the working title of the book while it was being writ ten was "Some Things You Can Do with 8L(2). " Some of the applications are outside representation theory, and some are to representation theory it self. The topics outside representation theory are mostly ones of substantial classical importance (Fourier analysis, Laplace equation, Huyghens' prin ciple, Ergodic theory), while the ones inside representation theory mostly concern themes that have been central to Harish-Chandra's development of harmonic analysis on semisimple groups (his restriction theorem, regularity theorem, character formulas, and asymptotic decay of matrix coefficients and temperedness). We hope this mix of topics appeals to nonspecialists in representation theory by illustrating (without an interminable prolegom ena) how representation theory can offer new perspectives on familiar topics and by offering some insight into some important themes in representation theory itself. Especially, we hope this book popularizes Harish-Chandra's restriction formula, which, besides being basic to his work, is simply a beautiful example of Fourier analysis on Euclidean space. We also hope representation theorists will enjoy seeing examples of how their subject can be used and will be stimulated by some of the viewpoints offered on representation-theoretic issues.
Book Synopsis Lectures in Modern Analysis and Applications I by : M. F. Atiyah
Download or read book Lectures in Modern Analysis and Applications I written by M. F. Atiyah and published by Springer. This book was released on 2006-12-08 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: This lecture series was presented by a consortium of universities in conjunction with the U.S. Air Force Office of Scientific Research during the period 1967-1969 in Washington, D.C. and at the University of Maryland. The series of lectures was devoted to active basic areas of contemporary analysis which is important in or shows potential in real-world applications. Each lecture presents a survey and critical review of aspects of the specific area addressed, with emphasis on new results, open problems, and applications. This volume contains nine lectures in the series; subsequent lectures will also be published.
Book Synopsis An Introduction to Harmonic Analysis on Semisimple Lie Groups by : V. S. Varadarajan
Download or read book An Introduction to Harmonic Analysis on Semisimple Lie Groups written by V. S. Varadarajan and published by Cambridge University Press. This book was released on 1999-07-22 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now in paperback, this graduate-level textbook is an introduction to the representation theory of semi-simple Lie groups. As such, it will be suitable for research students in algebra and analysis, and for research mathematicians requiring a readable account of the topic. The author emphasizes the development of the central themes of the sunject in the context of special examples, without losing sight of its general flow and structure. The book concludes with appendices sketching some basic topics with a comprehensive guide to further reading.
Book Synopsis Clifford Algebras and Dirac Operators in Harmonic Analysis by : John E. Gilbert
Download or read book Clifford Algebras and Dirac Operators in Harmonic Analysis written by John E. Gilbert and published by Cambridge University Press. This book was released on 1991-07-26 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to unite the seemingly disparate topics of Clifford algebras, analysis on manifolds, and harmonic analysis. The authors show how algebra, geometry, and differential equations play a more fundamental role in Euclidean Fourier analysis. They then link their presentation of the Euclidean theory naturally to the representation theory of semi-simple Lie groups.
Book Synopsis The Theory of Unitary Group Representations by : George Whitelaw Mackey
Download or read book The Theory of Unitary Group Representations written by George Whitelaw Mackey and published by . This book was released on 1955 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Analysis IV written by Roger Godement and published by Springer. This book was released on 2015-04-30 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis Volume IV introduces the reader to functional analysis (integration, Hilbert spaces, harmonic analysis in group theory) and to the methods of the theory of modular functions (theta and L series, elliptic functions, use of the Lie algebra of SL2). As in volumes I to III, the inimitable style of the author is recognizable here too, not only because of his refusal to write in the compact style used nowadays in many textbooks. The first part (Integration), a wise combination of mathematics said to be `modern' and `classical', is universally useful whereas the second part leads the reader towards a very active and specialized field of research, with possibly broad generalizations.
Book Synopsis Unitary Representations and Harmonic Analysis by : Mitsuo Sugiura
Download or read book Unitary Representations and Harmonic Analysis written by Mitsuo Sugiura and published by North Holland. This book was released on 1990 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: The principal aim of this book is to give an introduction to harmonic analysis and the theory of unitary representations of Lie groups. The second edition has been brought up to date with a number of textual changes in each of the five chapters, a new appendix on Fatou's theorem has been added in connection with the limits of discrete series, and the bibliography has been tripled in length.
Book Synopsis Geometric and Harmonic Analysis on Homogeneous Spaces by : Ali Baklouti
Download or read book Geometric and Harmonic Analysis on Homogeneous Spaces written by Ali Baklouti and published by Springer Nature. This book was released on 2019-08-31 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a number of important contributions focusing on harmonic analysis and representation theory of Lie groups. All were originally presented at the 5th Tunisian–Japanese conference “Geometric and Harmonic Analysis on Homogeneous Spaces and Applications”, which was held at Mahdia in Tunisia from 17 to 21 December 2017 and was dedicated to the memory of the brilliant Tunisian mathematician Majdi Ben Halima. The peer-reviewed contributions selected for publication have been modified and are, without exception, of a standard equivalent to that in leading mathematical periodicals. Highlighting the close links between group representation theory and harmonic analysis on homogeneous spaces and numerous mathematical areas, such as number theory, algebraic geometry, differential geometry, operator algebra, partial differential equations and mathematical physics, the book is intended for researchers and students working in the area of commutative and non-commutative harmonic analysis as well as group representations.
Book Synopsis Theory of Group Representations and Applications by : Asim Orhan Barut
Download or read book Theory of Group Representations and Applications written by Asim Orhan Barut and published by World Scientific. This book was released on 1986 with total page 750 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie!algebras - Topological!groups - Lie!groups - Representations - Special!functions - Induced!representations.
